Forced and thermocapillary convection in silicon Czochralski crystal growth in semispherical crucible

Abstract

Abstract. In order to understand the influence of a semispherical crucible geometry combined with different convection modes as a thermocapillary convection, natural convection and forced convection, induced by crystal rotation, on melt flow pattern in silicon Czochralski crystal growth process, a set of numerical simulations are conducted using Fluent Software. We solve the system of equations of heat and momentum transfer in classical geometry as cylindrical and modified crystal growth process geometry as cylindro-spherical. In addition, we adopt hypothesis adapted to boundary conditions near the interface and calculations are executed to determine temperature, pressure and velocity fields versus Grashof and Reynolds numbers. The analysis of the obtained results led to conclude that there is advantage to modify geometry in comparison with the traditional one. The absence of the stagnation regions of fluid in the hemispherical crucible corner and the possibility to control the melt flow using the crystal rotation enhances the quality of the process comparatively to the cylindrical one. The pressure field is strongly related to the swirl velocity.

Three‐dimensional study of the pressure field and advantages of hemispherical crucible in silicon Czochralski crystal growth

“…On the other hand the isotherms remain the same in the bulk flow and at the free surface which means that temperature field is not affected by thermocapillary convection. We note also the appearance of an inclusion corresponding to the higher pressures in the melt, situated at the triple point, this property confirms the two-dimensional results obtained before [10,11].…”

“…Fixed temperatures are imposed on the walls of the melt crucible and the crystal melt interface. In our previous works [10,11] we presented the equations for the fluid motion (Navier Stokes with the Boussinesq approximation) and temperature field with two-dimension axisymmetric assumption ( 0 φ ∂ ∂ = ). The three-dimensionless governing equations with non-axisymmetric assumption ( 0 φ ∂ ∂ ≠ ) [14] are,…”

“…However, surprisingly, two very important factors have not been considered enough in Czochralski crystal growth studies: the pressure and the spherical geometry. First, we conducted analytical works in this new configuration [8,9], then we performed two-dimensionnal numerical calculations [10,11] in an axisymetrical assumption.…”

Combined effects of crucible geometry and Marangoni convection on silicon Czochralski crystal growth

“…P. Anselmo et al [9] and M. H. Tavakoli et al [10] showed that a cylindrical crucible with a curved bottom has advantages for crystallization. Therefore, it is proposed recently by F. Mokhtari et al [11,12] to modify the device as a cylindro-spherical system. To facilitate the procedure of modelling related to the considered problem, we impose some assumptions; the molten silicon is assumed to be a viscous, Newtonian and incompressible fluid satisfying the Boussinesq assumption.…”

Numerical investigation of magnetic field effect on pressure in cylindrical and hemispherical silicon CZ crystal growth

“…The effect of magnetic field on temperature and flow fields has been considered by many researchers 1–11, while the pressure which is a key parameter in the growth process in natural, thermocapillary and forced convection modes 12 has not been studied under the influence of a magnetic field to our best knowledge. In addition, the silicon Czochralski crystal growth in spherical crucible is found to be of better advantages relatively to the cylindrical system when the magnetic field is not applied 12–16. This paper presents results of time‐dependent numerical simulations using the finite volume package Fluent in two different geometries, cylindro‐spherical and cylindro‐cylindrical with crystal and crucible rotation and Marangoni convection at the free surface.…”